Average Error: 62.0 → 62.0
Time: 2.4s
Precision: 64
Internal Precision: 128
\[\frac{x - lo}{hi - lo}\]
↓
\[\frac{x - lo}{hi - lo}\]

Error

Bits error versus lo

Bits error versus hi

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 62.0

    \[\frac{x - lo}{hi - lo}\]

  2. Initial simplification62.0

    \[\leadsto \frac{x - lo}{hi - lo}\]

  3. Final simplification62.0

    \[\leadsto \frac{x - lo}{hi - lo}\]

Runtime

Time bar (total: 2.4s)Debug log

start57.0ms

Algorithm
intervals

setup32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 62.0b

localize18.0ms

Local error

Found 1 expressions with local error:

62.0b
(/ (- x lo) (- hi lo))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 34
Calls

1 calls. Slowest were:

4.0ms
(/ (- x lo) (- hi lo))

series51.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

51.0ms
(/ (- x lo) (- hi lo))

simplify462.0ms

Counts
33 → 37
Calls

33 calls. Slowest were:

207.0ms
(/ (* (* (- x lo) (- x lo)) (- x lo)) (* (* (- hi lo) (- hi lo)) (- hi lo)))
37.0ms
(/ (* (cbrt (- x lo)) (cbrt (- x lo))) 1)
25.0ms
(+ (* hi hi) (+ (* lo lo) (* hi lo)))

prune271.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 62.0b

herbie shell --seed 2018359 +o rules:numerics
(FPCore (lo hi x)
  :name "(/ (- x lo) (- hi lo))"
  :pre (and (< lo -1e+308) (> hi 1e+308))
  (/ (- x lo) (- hi lo)))